Let's do this question, Esquire style of length, 20 centimeter as four quarter circles at each corner
as shown in the figure.
Find the area of the shaded portion.
Now, that's the spot over here.
All right.
Another tile with the same dimensions has a circle in the center of the tile.
This is the second one.
All right.
Is the first one.
Is the second one.
Now, if the circle touches all the four sides of the square to find the area of the shaded portion,
which is this part way here in which tile area of the shaded portion will be more.
Remember, we have already discussed this.
It will be the same, right.
If you join this and this together, you will see that this part over here.
And if I join it over here also.
You will see we have discussed that this and this are equal right now, let's see it again so that you
solidify your understanding.
Now, I'm already telling you the answer.
You should be able to do this question in five seconds because we have already discussed it.
But let's again discuss it.
This case one is this case two.
All right.
Now, the area of the trial is 20 to 20 because it's a square, right.
That's equal to 400 centimetre square.
All right.
Now, over here, this is the radius, right?
So let me marketers are so this is also equal to our two hour is equal to 20.
Therefore, are is equal to 10 centimetre.
Right.
All right.
So what would be this area?
This area will be won by sort of by our square.
Right, because this is a quarter of a circle.
So one by four off by our square where all is equal to 10.
Now, if you want all these four together, you need to multiply this with four.
That's four in the one by four into Pyar Square, which is the same as by our square.
Right.
All right.
Now that that would be three point one four into 10 square, which is approximately three hundred and
fourteen centimeter square, so what's the answer?
The shaded region will be four hundred minus three, one four.
And remember, it's this part that was shaded in the question that's 400 minus three hundred and fourteen,
which is approximately eight to six centimeters square.
Now I tell approximately because three point one four is the approximate value of PI.
All right.
Now, let's see the second case over here, the diameter is two are and two are again, is equal to
20.
So odd is equal to ten.
And the area of the circle will be Pyar Square.
Right.
That also is equal to three hundred and fourteen.
Therefore, over here also it's 400 minus three hundred and fourteen which is equal to eighty six centimeters
square.
And you can see that the shaded region in both the cases is equal.